A Survey on Kolmogorov-Arnold Network

This systematic review explores the theoretical foundations, evolution,applications, and future potential of Kolmogorov-Arnold Networks (KAN), aneural network model inspired by the Kolmogorov-Arnold representation theorem.KANs distinguish themselves from traditional neural networks by usinglearnable, spline-parameterized functions instead of fixed activationfunctions, allowing for flexible and interpretable representations ofhigh-dimensional functions. This review details KAN’s architectural strengths,including adaptive edge-based activation functions that improve parameterefficiency and scalability in applications such as time series forecasting,computational biomedicine, and graph learning. Key advancements, includingTemporal-KAN, FastKAN, and Partial Differential Equation (PDE) KAN, illustrateKAN’s growing applicability in dynamic environments, enhancinginterpretability, computational efficiency, and adaptability for complexfunction approximation tasks. Additionally, this paper discusses KAN’sintegration with other architectures, such as convolutional, recurrent, andtransformer-based models, showcasing its versatility in complementingestablished neural networks for tasks requiring hybrid approaches. Despite itsstrengths, KAN faces computational challenges in high-dimensional and noisydata settings, motivating ongoing research into optimization strategies,regularization techniques, and hybrid models. This paper highlights KAN’s rolein modern neural architectures and outlines future directions to improve itscomputational efficiency, interpretability, and scalability in data-intensiveapplications.

Further reading#

• Access Paper in arXiv.org